This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071723 #19 Jul 13 2025 13:05:54
%S A071723 1,4,15,54,192,682,2431,8710,31382,113696,414086,1515516,5571750,
%T A071723 20569590,76228095,283481670,1057628550,3957577800,14849601090,
%U A071723 55859886420,210622646520,795898303668,3013646759910,11432740177564,43448822603452,165396657221152
%N A071723 Expansion of (1+x^2*C^2)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F A071723 a(n) = (Sum_{k=0..n} (k+1)*(k^2+k+1)*binomial(2*n-k,n))/(n+1). - _Vladimir Kruchinin_, Sep 28 2011
%F A071723 a(n) = (4*binomial(2*n+3,n)+6*binomial(2*n+1,n+3))/(n+4). - _Tani Akinari_, Dec 01 2024
%F A071723 D-finite with recurrence 2*(n+4)*a(n) +2*(-7*n-16)*a(n-1) +3*(9*n+4)*a(n-2) +6*(-2*n+3)*a(n-3)=0. - _R. J. Mathar_, Jul 13 2025
%p A071723 a := n -> (2*(2*n + 1)*(11*n^2 + 17*n + 12)*binomial(2*n, n))/((n + 1)*(n + 2)*(n + 3)*(n + 4)): seq(a(n), n = 0..25); # _Peter Luschny_, Dec 01 2024
%o A071723 (Maxima) a(n):=sum((k+1)*(k^2+k+1)*binomial(2*n-k,n),k,0,n)/(n+1); /* _Vladimir Kruchinin_, Sep 28 2011 */
%o A071723 (Maxima) a(n):=(4*binomial(2*n+3,n)+6*binomial(2*n+1,n+3))/(n+4); /* _Tani Akinari_, Dec 01 2024 */
%Y A071723 gf=(1+x^2*C^2)*C^m: A000782 (m=1), A071721 (m=2), A071722 (m=3), this sequence (m=4).
%Y A071723 Cf. A000108.
%K A071723 nonn
%O A071723 0,2
%A A071723 _N. J. A. Sloane_, Jun 06 2002